Flow of multiphase mixtures

It is required to transport sand of particle size 1.25 mm and density 2600 kg/m at the rate of 1 kg/s through a horizontal pipe 200 m long. Estimate the air flowrate required, the pipe diameter, and the pressure drop in the pipe-line. 

For conventional pneumatic transport in pipelines, a solids-gas mass ratio of about 5 is employed. Mass flow of air = (1/5) = 0.20 kg/s 

In order to avoid excessive pressure drops, an air velocity of 30 m/s seems reasonable. Ignoring the volume occupied by the sand (which is about 0.2% of that occupied by the air), the cross-sectional area of pipe required = (0.20/30) = 0.0067 m, equivalent to a pipe diameter of V(4 x 0.0067/jr) = 0.092 m or 92 mm. 

From Table 5.3 for sand of particle size 1.25 mm and density 2600 kg/m, the free-falling velocity is  

Sand of a mean diameter 0.2 mm is to be conveyed in water flowing at 0.5 kg/s in a 25 mm ID horizontal pipe 100 m long. What is the maximum amount of sand which may be transported in this way if the head developed by the pump is limited to 300 kN/m Assume fully suspended heterogeneous flow. 

The flow problems considered in previous chapters are concerned with homogeneous fluids, either single phases or suspensions of fine particles whose settling velocities are sufficiently low for the solids to be completely suspended in the fluid. Consideration is now given to the far more complex problem of the flow of multiphase systems in which the composition of the mixture may vary over the cross-section of the pipe or channel furthermore, the components may be moving at different velocities to give rise to the phenomenon of slip between the phases. 

Multiphase flow is important in many areas of chemical and process engineering and the behaviour of the material will depend on the properties of the components, the flowrates and the geometry of the system. In general, the complexity of the flow is so great that design methods depend very much on an analysis of the behaviour of such systems in practice and, only to a limited extent, on theoretical predictions. Some of the more important systems to be considered are  

Liquids mixed with solid particles ( hydraulic transport ). 

Gases carrying solid particles wholly or partly in suspension ( pneumatic transport ). 

Multiphase systems containing solids, liquids and gases. 

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